| Title:
|
Some remarks on quaternion-Hermitian manifolds (English) |
| Author:
|
Swann, Andrew |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
349-354 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Nearly-quaternionic Kähler manifolds of dimension at least $8$ are shown to be quaternionic Kähler. Restrictions on the covariant derivative of the fundamental four-form of a semi-quaternionic Kähler are also found. (English) |
| Keyword:
|
G-structure |
| Keyword:
|
quaternion-Hermitian manifold |
| Keyword:
|
nearly-quaternionic Kähler |
| Keyword:
|
semi-quaternionic Kähler |
| Keyword:
|
fundamental four-form |
| MSC:
|
53C15 |
| MSC:
|
53C25 |
| MSC:
|
53C55 |
| idZBL:
|
Zbl 0910.53023 |
| idMR:
|
MR1601349 |
| . |
| Date available:
|
2008-06-06T21:34:40Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107623 |
| . |
| Reference:
|
[B] Bonan, E.: Sur l’algèbre extérieure d’une variété presque hermitienne quaternionique.C. R. Acad. Sci. Paris 295 (1982), 115–118. MR 0676377 |
| Reference:
|
[BtD] Bröcker, T., tom Dieck, T.: Representations of Compact Lie Groups.Graduate Texts in Math., 98, Springer, 1985. MR 0781344 |
| Reference:
|
[C] Cabrera, F. M.: Variedades cuaternionicas y $G_2$-variadades.Ph. D. Thesis, Univ. de La Laguna. |
| Reference:
|
[I] Ishihara, S.: Quaternion Kählerian manifolds.J. Differ. Geom. 9 (1974), 483–500. Zbl 0297.53014, MR 0348687 |
| Reference:
|
[M] Moreiras, B. R.: Variedades cuaterniónicas no-kählerianas.Publ. Depto. Geom. y Top., Univ. de Santiago 62 (1984). |
| Reference:
|
[Sa] Salamon, S. M.: Quaternionic Kähler manifolds.Invent. Math. 67 (1982), 143–171. Zbl 0486.53048, MR 0664330 |
| Reference:
|
[Sw1] Swann, A. F.: Aspects symplectiques de la géométrie quaternionique.C. R. Acad. Sci. Paris 308 (1989), 225–228. Zbl 0661.53023, MR 0986384 |
| Reference:
|
[Sw2] Swann, A. F.: Quaternionic Kähler geometry and the fundamental $4$-from.Proceedings of the Curvature Geometry Workshop, Lancaster, C. T. J. Dodson (ed.), UDLM Publ., 1989, pp. 165–174. MR 1089891 |
| Reference:
|
[Sw3] Swann, A. F.: HyperKähler and quaternionic Kähler geometry.Math. Ann. 289 (1991). Zbl 0711.53051, MR 1096180 |
| . |
